Neuroimaging data have been widely used to derive possible biomarkers for Alzheimer’s Disease (AD) diagnosis. As only certain brain regions are related to AD progression, many feature selection methods have been proposed to identify informative features (i.e., brain regions) to build an accurate prediction model. These methods mostly only focus on the feature-target relationship to select features which are discriminative to the targets (e.g., diagnosis labels). However, since the brain regions are anatomically and functionally connected, there could be useful intrinsic relationships among features. In this paper, by utilizing both the feature-target and feature-feature relationships, we propose a novel sparse regression model to select informative features which are discriminative to the targets and also representative to the features. We argue that the features which are representative (i.e., can be used to represent many other features) are important, as they signify strong “connection” with other ROIs, and could be related to the disease progression. We use our model to select features for both binary and multi-class classification tasks, and the experimental results on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset show that the proposed method outperforms other comparison methods considered in this work.